Compensating body motion in medical imaging is a necessity and has already become indispensable in this area. Since motion compensation by rigid or affine transformations is suitable only for few clinical target applications (e.g. patient positioning for brain applications), motion compensation by a non-rigid or elastic transformation has become state-of-the-art. A prominent example for the usefulness of an elastic transformation is respiratory motion.
Motion compensation requires the registration of at least two images for computing a deformation vector field (DVF) that aligns one image according to a second image. As a necessary criterion for a successful registration, the smallness of the residuum image (i.e., of the subtraction of the aligned first image and second image) can be used. Misaligned image structures are visible as remaining shadows in the residuum. However, the absence of any structure in the residuum image does not guarantee a successful registration since the residuum is invariant to the deformation of homogeneous image regions.
Typically, an image registration scheme aims at balancing two types of forces: an outer force driven by the difference of the two images and an inner force driven by a physical model. Consequently, a weighting factor is introduced to balance these two forces. Generally, the application of a large weight on the outer force is likely to yield a small residuum image. Unfortunately, it often introduces incorrect deformations, even folding, into the DVF. Therefore, using a residuum image for validating a DVF may often lead to an erroneous determination of the DVF.